How to create a hologram projection with light rays?
Here's the result I got:



And here are my nodes:



Note: the Translate and Scale group nodes are homemade equivalents of the corresponding parts of the mapping node.  They are explained here.  I am using them here because they allow me to plug inputs into the transform values instead of being static like the mapping node is.

The basic idea is to use a noise texture to drive the emission strength of a volumetric emission material on a cone (actually a frustum).  The noise texture is scaled up on the z-axis to create the vertical stripes.  The real trick is to get the stripes to angle out from a point instead of just going straight up, and that is what all those other nodes are doing.  (Sorry for the massive node spaghetti, I had to move them around to get it to all fit on my screen and be readable.)

Here's the basic flow:


Start with generated mapping coordinates and scale the z-axis up (smaller scale value) to make the vertical stripes.  The Translate node is just to move the origin of the coordinates to the XY center of the object (i.e. center of the base of the object).
The Z component of the generated coordinates is extracted to use as a vertical linear gradient to scale the rays in towards the bottom, which has the effect of slanting them out from the base.  The RGB Curves node remaps the gradient from 0.0-1.0 to 0.5-1.0, I am using 0.5 because the base of my frustum is one half (0.5) the diameter of the top of the frustum.  The Math > Divide node is used to invert the scale factor since we want to scale the texture in instead of the texture coordinates.
The resulting mashed-up texture coordinates are used for a noise texture.  The color ramp node is used to adjust the contrast of the rays (i.e. make it look more ray-like).
To get the rays to fade out vertically instead of coming to an abrupt stop at the top of the mesh I used the generated coordinates z-component gradient again. The RGB Curves node is to reverse the gradient and make adjust the falloff curve.  By multiplying it with the rays from the Color Ramp I created the desired falloff.
The final Multiply node is to adjust the overall brightness/strength of the rays.


Here is a .blend:



The above .blend contains a couple of enhancements.  I set up a very simple armature to make adjusting the size and shape of the beam easier.  I set up some drivers in the material so that the scale values are adjusted to match the armature-deformed frustum.  It also contains the rest of the above scene.